Abstract
A reliable forecasting model for each Water Treatment Plant (WTP) influent characteristics is useful for controlling the plant’s operation. In this paper Auto-Regressive Integrated Moving Average (ARIMA) and Neural Network Auto-Regressive (NNAR) modeling techniques were applied on a WTP’s influent water characteristics time series to make some models for short-term period (to seven days ahead) forecasting. The ARIMA and NNAR models both provided acceptable generalization capability with R2s ranged from 0.44 to 0.91 and 0.45 to 0.92, respectively, for chloride and temperature. Although a more prediction performance was observed for NNAR in comparison with ARIMA for all studied series, the forecasting performance of models was further examined using Time Series Cross-Validation (TSCV) and Diebold-Mariano test. The results showed ARIMA is more accurate than NNAR for forecasting the horizon-daily values for CO2, Cl and Ca time-series. Therefore, despite of the good predictive performance of NNAR, ARIMA may still stands as better alternative for forecasting task of aforementioned series. Thus, as a general rule, not only the predictive performance using R2 statistic but also the forecasting performance of a model using TSCV, are need to be examined and compared for selecting an appropriate forecasting model for WTP’s influent characteristics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike, H. (1974). “A new look at the statistical model identification.” Automatic Control, IEEE Transactions on, Vol. 19, No. 6, pp. 716–723, DOI: 10.1109/TAC.1974.1100705.
Battiti, R. (1992). “First-and second-order methods for learning: Between steepest descent and Newton’s method.” Neural Computation, Vol. 4, No. 2, pp. 141–166, DOI: 10.1162/neco.1992.4.2.141.
Box, G. E. and Cox, D. R. (1964). “An analysis of transformations.” Journal of the Royal Statistical Society. Series B (Methodological), Vol. 26, No. 2, pp. 211–252.
Box, G. E., Jenkins, G. M., and Reinsel, G. C. (2013). Time series analysis: Forecasting and control, John Wiley & Sons, DOI: 10.1002/9781118619193.
Diebold, F. X. and Mariano, R. S. (1995). “Comparing predictive accuracy.” Journal of Business & Economic Statistics, Vol. 13, pp. 253–265, DOI: 10.1198/073500102753410444.
Durbin, J. and Watson G. S. (1950). “Testing for serial correlation in least squares regression: I.” Biometrika, Vol. 37, Nos. 3–4, pp. 409–428, DOI: 10.2307/2332391.
Field, A. (2009). Discovering statistics using SPSS:(and sex and drugs and rock ‘n’roll). 3rd ed, Sage, Los Angeles.
Hadi, M., Mesdaghinia, A., Yunesian, M., Nasseri, S., Nodehi, R. N., Tashauoei, H., Jalilzadeh, E., and Zarinnejad, R. (2016). “Contribution of environmental media to cryptosporidiosis and giardiasis prevalence in Tehran: A focus on surface waters.” Environmental Science and Pollution Research, Vol. 23, No. 19, pp. 19317–19329, DOI: 10.1007/s11356-016-7055-9.
Hagan, M. T., Demuth, H. B., and Beale, M. H. (1996). Neural network design, Thomson Learning, Singapore.
Hill, T., Marquez, L., O’Connor, M., and Remus, W. (1994). “Artificial neural network models for forecasting and decision making.” International Journal of Forecasting, Vol. 10, No. 1, pp. 5–15, DOI: 10.1016/0169–2070(94)90045–0.
Ho, S. L., Xie, M., and Goh, T. N. (2002). “A comparative study of neural network and Box-Jenkins ARIMA modeling in time series prediction.” Computers & Industrial Engineering, Vol. 42, Nos. 2–4, pp. 371–375, DOI: 10.1016/S0360–8352(02)00036–0.
Hosseini, H. G., Luo, D., and Reynolds, K. J. (2006). “The comparison of different feed forward neural network architectures for ECG signal diagnosis.” Medical Engineering & Physics, Vol. 28, No. 4, pp. 372–378, DOI: 10.1016/j.medengphy.2005.06.006.
Howard, D. and Mark, B. (2000). Neural Network Toolbox For Use with MATLAB: Computation Visualization, Programming, User’s Guide Version 4, MathWorks, Inc.
Hyndman, R. J. and Khandakar, Y. (2007). “Automatic time series for forecasting: The forecast package for R.” Journal of Statistical Softwore, Vol. 27, No. 3, DOI: 10.18637/jss.vo27.i03.
Hyndman, R. J. and Koehler A. B. (2006). “Another look at measures of forecast accuracy.” International Journal of Forecasting, Vol. 22, No. 4, pp. 679–88, DOI: 10.1016/j.ijforecast.2006.03.001.
Franses, P. H. (2016). “A note on the mean absolute scaled error.” International Journal of Forecasting, Vol. 32, No. 1, pp. 20–22, DOI: 10.1016/j.ijforecast.2015.03.008.
Jafari Mansoorian, H., Karimaeec, M., Hadi, M., Jame Porazmey, E., Barati, F., and Baziar, M. (2017). “Feed forward artificial neural network model to estimate the TPH removal efficiency in soil washing process.” Archives of Hygiene Sciences, Vol. 6, No. 1, pp. 69–104.
Khashei, M. and Bijari, M. (2010). “An artificial neural network (p, d, q) model for timeseries forecasting.” Expert Systems with Applications, Vol. 37, No. 1, 479–489, DOI: 10.1016/j.eswa.2009.05.044.
Khodadadi, M., Mesdaghinia, A., Nasseri, S., Ghaneian, M. T., Ehrampoush, M. H., and Hadi, M. (2016). “Prediction of the waste stabilization pond performance using linear multiple regression and multi-layer perceptron neural network: A case study of Birjand.” Iran. Environmental Health Engineering and Management Journal, Vol. 3, pp. 81–89.
Khashei, M. and Bijari, M. (2011). “A novel hybridization of artificial neural networks and ARIMA models for time series forecasting.” Applied Soft Computing, Vol. 11, No. 2, pp. 2664–2675, DOI: 10.1016/j.asoc.2010.10.015.
Kusiak, A., Verma, A., and Wei, X. (2012). “A data-mining approach to predict influent quality.” Environmental Monitoring and Assessment, Vol. 185, pp. 2197–2210, DOI: 10.1007/s10661-012-2701-2.
Ljung, G. M. and Box, G. E. (1978). “On a measure of lack of fit in time series models.” Biometrika, Vol. 65, No. 2, pp. 297–303, DOI: 10.1093/biomet/65.2.297.
Maest, A. S., Kuipers J., Travers C. L., and Atkins D. A. (2005). Predicting Water Quality at Hardrock Mines: Methods and Models, Uncertainties and State-of-the-art, Earthworks, Washington, DC.
Matalas, N. (1967). “Time series analysis.” Water Resources Research, Vol. 3, No. 3, pp. 817–829, DOI: 10.1029/WR003i003p00817.
Pankratz, A. (2009). Forecasting with univariate Box-Jenkins models: Concepts and cases, John Wiley & Sons, New Jersey.
Panno, S. V., Keith, C. H., Hwang, H. H., Greenberg, S., Krapac, I. G., Landsberger, S., and O’Kelly, D. J. (2002). “Source identification of sodium and chloride contamination in natural waters: Preliminary results.” In Proceedings, 12th Annual Illinois Groundwater Consortium Symposium, Illinois Groundwater Consortium.
Plazl, I., Pipus, G., Drolka, M., and Koloini, T. (1999). “Parametric sensitivity and evaluation of dynamic model for single-stage wastewater treatment plant.” Acta Chimica Slovenica, Vol. 46, No. 2, pp. 289–300.
R Core Team (2016). R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. URL: https://doi.org/www.R-project.org.
Rostami Fasih, Z., Mesdaghinia, A., Nadafi, K., Nabizadeh Nodehi, R., Mahvi, A. H., and Hadi, M. (2015). “Forecasting the air quality index based on meteorological variables and autocorrelation terms using artificial neural network.” Razi Journal of Medical Sciences, Vol. 22, No. 137, pp. 31–43.
Rumelhart, D. E. and McClelland, J. L. (1986). Parallel distributed processing: Explorations in the microstructure of cognition: Foundations, MIT Press Cambridge, MA, USA.
Salas, J. D. Obeysekera J. (1982). “ARMA model identification of hydrologic time series.” Water Resources Research, Vol. 18, No. 4, pp. 1011–1021, DOI: 10.1029/WR018i004p01011.
Salas, J. D. (1980). Applied modeling of hydrologic time series, Water Resources Publication.
Salas, J. D., Boes, D. C., and Smith, R. A. (1982). “Estimation of ARMA models with seasonal parameters.” Water Resources Research, Vol. 18, No. 4, pp. 1006–1010, DOI: 10.1029/WR018i004p01006.
Solaimany-Aminabad, M., Maleki, A., and Hadi, M. (2013). “Application of Artificial Neural Network (ANN) for the prediction of water treatment plant influent characteristics.” Journal of Advances in Environmental Health Research, Vol. 1, No. 2, pp. 89–100, DOI: 10.22102/jaehr.2013.40130.
Thoplan, R. (2014). “Simple v/s sophisticated methods of forecasting for mauritius monthly tourist arrival data.” International Journal of Statistics and Applications, Vol. 4, No. 5, pp. 217–223, DOI: 10.5923/j.statistics.20140405.01.
Valipour, M., Banihabib, M. E., and Behbahani, S. M. R. (2013). “Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir.” Journal of Hydrology, Vol. 476, pp. 433–441, DOI: 10.1016/j.jhydrol.2012.11.017.
Wu, G.-D. and Lo, S.-L. (2008). “Predicting real-time coagulant dosage in water treatment by artificial neural networks and adaptive networkbased fuzzy inference system.” Engineering Applications of Artificial Intelligence, Vol. 21, No. 8, pp. 1189–1195, DOI: 10.1016/j.engappai.2008.03.015.
Wu, G.-D. and Lo, S.-L. (2010). “Effects of data normalization and inherentfactor on decision of optimal coagulant dosage in water treatment by artificial neural network.” Expert Systems with Applications, Vol. 37, No. 7, pp. 4974–4983, DOI: 10.1016/j.eswa.2009.12.016.
Zhang, G., Eddy Patuwo, B. and Y Hu M. (1998). “Forecasting with artificial neural networks: The state of the art.” International Journal of Forecasting, Vol. 14, No. 1, pp. 35–62, DOI: 10.1016/S0169-2070(97)00044-7.
Zhang, G. P. (2003). “Time series forecasting using a hybrid ARIMA and neural network model.” Neurocomputing, Vol. 50, pp.159–175, DOI: 10.1016/S0925-2312(01)00702-0.
Zhang, G. P. and Qi, M. (2005). “Neural network forecasting for seasonal and trend time series.” European Journal of Operational Research, Vol. 160, No. 2, pp. 501–514, DOI: 10.1016/j.ejor.2003.08.037.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Maleki, A., Nasseri, S., Aminabad, M.S. et al. Comparison of ARIMA and NNAR Models for Forecasting Water Treatment Plant’s Influent Characteristics. KSCE J Civ Eng 22, 3233–3245 (2018). https://doi.org/10.1007/s12205-018-1195-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-018-1195-z